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Simplifying x2 + 3x + -112 = 0 Reorder the terms: -112 + 3x + x2 = 0 Solving -112 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 3x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 3x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 3x + x2 = 0 + 112 3x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 3x + x2 = 112 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 112 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 112 + 2.25 Combine like terms: 112 + 2.25 = 114.25 2.25 + 3x + x2 = 114.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + 1.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + 1.5 = 10.688779163 Simplifying x + 1.5 = 10.688779163 Reorder the terms: 1.5 + x = 10.688779163 Solving 1.5 + x = 10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.688779163 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.688779163 + -1.5 x = 10.688779163 + -1.5 Combine like terms: 10.688779163 + -1.5 = 9.188779163 x = 9.188779163 Simplifying x = 9.188779163Subproblem 2
x + 1.5 = -10.688779163 Simplifying x + 1.5 = -10.688779163 Reorder the terms: 1.5 + x = -10.688779163 Solving 1.5 + x = -10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.688779163 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.688779163 + -1.5 x = -10.688779163 + -1.5 Combine like terms: -10.688779163 + -1.5 = -12.188779163 x = -12.188779163 Simplifying x = -12.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.188779163, -12.188779163}
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